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(sqrt15+sqrt35+sqrt21+5)/(sqrt3+2sqrt5+s...

`(sqrt15+sqrt35+sqrt21+5)/(sqrt3+2sqrt5+sqrt7)=?`

A

`N + (1)/(N) = 7`

B

`N^(2) + (1)/(N^(2)) = 5`

C

`N^(3) + (1)/(N^(3)) = 9`

D

`N^(4) + (1)/(N^(4)) = 23`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`N=(sqrt(3)+sqrt(5)+sqrt(5)+sqrt7)/((sqrt(3)+sqrt(5))+(sqrt(5)+sqrt(7)))`
`rArr (1)/(N) = (1)/(sqrt(5) + sqrt(7)) + (1)/(sqrt(5) + sqrt(3))`
`= (1)/(2) (sqrt(7) - sqrt(3)), N = (sqrt(7) + sqrt(3))/(2)`
`N + (1)/(N) = sqrt(7)`
`N^(2) + (1)/(N^(2)) = (N + (1)/(N))^(2) -2 = 5`
`(N^(4) + (1)/(N^(4))) = (N^(2) + (1)/(N^(2)))^(2) - 2 = 23`
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